Select the equivalent expression. (x^(-2)*x^(-5))/(x^(8)) (1)/(x^(15)) x^(15) x (1)/(x)

Simplify Exponents: We need to simplify the expression (x^(-2)*x^(-5))/(x^(8)). According to the properties of exponents, when we multiply two exponents with the same base, we add the exponents. Calculation: x^(-2) * x^(-5) = x^(-2 + -5) = x^(-7)Combine Exponents: Now we have x^(-7) divided by x^(8). According to the properties of exponents, when we divide two exponents with the same base, we subtract the exponents in the denominator from the exponents in the numerator. Calculation: x^(-7) / x^(8) = x^(-7 - 8) = x^(-15)Rewrite Negative Exponent: The expression x^(-15) can be rewritten as 1/(x^(15)) because any negative exponent indicates that the base is on the opposite side of the fraction line. Calculation: x^(-15) = 1/(x^(15))

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Select the equivalent expression.

(x^(-2)*x^(-5))/(x^(8))

(1)/(x^(15))

x^(15)

x

(1)/(x)

Select the equivalent expression. $\newline$ $\frac{x^{-2} \cdot x^{-5}}{x^{8}}$ $\newline$ $\frac{1}{x^{15}}$ $\newline$ $x^{15}$ $\newline$ $x$ $\newline$ $\frac{1}{x}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\frac{x^{-2} \cdot x^{-5}}{x^{8}}

\newline

\frac{1}{x^{15}}

\newline

x^{15}

\newline

x

\newline

\frac{1}{x}

Simplify Exponents: We need to simplify the expression $(x^{-2}\cdot x^{-5})/(x^{8})$ . According to the properties of exponents, when we multiply two exponents with the same base, we add the exponents. $\newline$ Calculation: $x^{-2} \cdot x^{-5} = x^{-2 + -5} = x^{-7}$
Combine Exponents: Now we have $x^{-7}$ divided by $x^{8}$ . According to the properties of exponents, when we divide two exponents with the same base, we subtract the exponents in the denominator from the exponents in the numerator. $\newline$ Calculation: $x^{-7} / x^{8} = x^{-7 - 8} = x^{-15}$
Rewrite Negative Exponent: The expression $x^{-15}$ can be rewritten as $\frac{1}{x^{15}}$ because any negative exponent indicates that the base is on the opposite side of the fraction line. $\newline$ Calculation: $x^{-15} = \frac{1}{x^{15}}$